Q1. I just want to make sure...Don't both eius, etc. and suus, etc. NOT follow the gender, number, and case of the subject or the person possessing, but they DO follow the gender, number, and case of the that which is being possessed, although they both have reference to the that which is doing the possessing?

Q2. If this is true, how can we know when to use the eius, eorum, earum, or the suus, sua, suum ? Are there certain rules I can follow to make the proper distinctions?

_________________"The only successful method will be that which bases harmony and agreement among Christ's faithful ones upon all the truths, and the whole of the truths, which God has revealed." -Pope Pius XII

Some of these ecumenists are so preoccupied with Christian unity that they are willing to destroy Catholic unity in the name of Christian unity. - Fr. John Hardon

It's maybe a little confusing because those words are two different parts of speech. You correctly note that suus, like other adjectives, corresponds in gender, number and case to the word it modifies. Hence a sentence like tunc loquetur ad eos in ira sua et in furore suo conturbabit eos. You see that suus matches the gender and case of the noun "being possesed" as you put it rather than the subject, namely, the Lord (Dominus).

Eius on the other hand is not a possessive adjective, but actually the singular genitive of the third-person pronoun is. This means that it will operate in the opposite manner of suus, conforming not to what is possessed, but to the possessor. It will always be genitive, so the case is constant. It only varies according to the gender and number of the possessor. See this table for declensions.

So when do you use which? Suus is "reflexive," which means that it is used when it corresponds to the subject of the relevant sentence or clause. For instance, Johannes canem suum amat means John loves his own dog. Eius on the other hand is just a simple third-person pronoun so Johannes canem eius amat would mean that John loves Bob's dog or whoever's dog it may happen to be (which would be clear from the broader context). More on reflexives: